Super Interesting Math Problem!.....that i need help with...?

Question

A bag contains twenty white balls and thirty black balls. Four balls are randomly drawn, with out replacement. What is the probability of selecting a white ball followed by a black ball, then a black ball followed by a white ball?

I have no idea...plz help if you can and explain..

Thank You!

Answer 1

The probability that the first ball is white is 20/50 = 2/5.

The conditional probability that the second ball is black is based on what fraction of the remaining 49 balls are black.

The conditional probability that the third ball is black is based on the colors of the remaining 48 balls.

And similarly for the last ball.

Then multiply the four probabilities you just computed. If the number is somewhat less than 1/16, there's a good chance you did it all correctly

Answer 2

So it's not enough to draw two white balls and two black balls; we need to draw the exact sequence of white-black-black-white.

There are initially 50 balls in total in the bag, so the proability of picking a white ball first is 20/50. The probabiltiy of picking a black ball next is 30/49 (remember that after you take out the first ball, there are only 49 balls left in the bag). Then to pick another black ball after that is 29/48, since at the start of the third turn we already removed one black ball earler and there are 48 balls in the bag total. Finally, after picking these 3 balls, the probability of getting a white ball next is 19/47.

Multiply all of these together, and you get (20/50)(30/49)(29/48)(19/47) = 551/9212, which is about 0.0598.

Answer 3

Just multiply the odds of each transaction.
20/50*30/49*29/48*19/47=0.0598, or about 6%.

Answer 4

Ah, not that interesting, but I'll help anyway.... :)

(20/50) * (30/49) * (29/48) * (19/47). Figure out the logic behind that, then crank out the calculation.

Answer 5

1st draw: 20w and 30b, so 20/50 for white
2nd draw: 19w and 30b, so 30/49 for black
3rd draw: 19w and 29b, so 29/48 for black
4th draw: 19w and 28b, so 19/47 for white

The total probability is the product of the individual probabilities, or:

20/50 * 30/49 * 29/48 * 19/47 = 5.981%

Best of luck! :)

Answer 6

(20/50) x (30/49) x (29/48) x (19/47)
W/total x B/remaining x remainingW/remainingTotal x remB/remTotal

Answer 7

there's an equation for this some thing like a!-n!/n!-1 or something.